KRUMME, GUNTER (University of Hawaii), Differentiation and Interaction in Three-Dimensional Space: Some Conceptual Speculations.

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The paper elaborates on some of the implications of a "Germanic Bias" in the development of theoretical human geography. Advances in location theory have been strictly limited to two-dimensional, horizontal space relationships dismissing physical features such as terrain as well as man-made vertical space relationships as "distortions." Particularly in an urban context the vertical dimension of space has become a significant economic variable. Two-dimensional urban land use and interaction models are recognized to be increasingly inadequate for comprehensive urban air- and space-use planning. The present use of largely two-dimensional population density concepts is a vivid example for this point.

Some aspects of residential space use have been analyzed in more detail. A substitution and indifference framework a la Alonso is proposed for the theoretical analysis of the forces behind the demand schedule for residential height. Preliminary empirical investigations suggest a number of factors, which may be responsible for demand and supply differentiation.

Economic aspects related to non-horizontal space dimensions and functional relationships are not restricted to high-rise residential decision-making. In many ways, residential land use variations on hills and slopes seem to be based on similar factors. For urban air pollution, road and air transportation, multi4evel circulation in cities, as well as mining operations and agricultural and recreational activities, height, depth and elevation in addition to slope gradients are crucial variables for the determination of private and social cost and benefit patterns. It is suggested that theory oriented geographers attempt to include the third dimension into traditional models in a more rigorous way than has been done so far.

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